Last updated on May 26th, 2025
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 1000000 and explain the methods used.
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In exponential form, ∛1000000 is written as 1000000(1/3).
The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 1000000, then y3 can be 1000000. Since 1000000 is a perfect cube, the cube root of 1000000 is exactly 100.
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 1000000. The common methods we follow to find the cube root are given below:
Since 1000000 is a perfect cube, the prime factorization method can be effectively used.
Let's find the cube root of 1000000 using the prime factorization method. First, express 1000000 as a product of its prime factors: 1000000 = 106 = (2 × 5)6 = 26 × 5^6
To find the cube root, we take one-third of the powers of each prime factor: ∛1000000 = 2^(6/3) × 5^(6/3) = 2^2 × 5^2 = 4 × 25 = 100 Therefore, the cube root of 1000000 is 100.
Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes students commonly make and the ways to avoid them:
Imagine you have a cube-shaped toy that has a total volume of 1000000 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛1000000 = 100 units
To find the side of the cube, we need to find the cube root of the given volume. Therefore, the side length of the cube is exactly 100 units.
A company manufactures 1000000 cubic meters of material. Calculate the amount of material left after using 500000 cubic meters.
The amount of material left is 500000 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount: 1000000 - 500000 = 500000 cubic meters.
A bottle holds 1000000 cubic centimeters of volume. Another bottle holds a volume of 200000 cubic centimeters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 1200000 cubic centimeters.
Explanation: Let’s add the volume of both bottles: 1000000 + 200000 = 1200000 cubic centimeters.
When the cube root of 1000000 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 100 = 200 The cube of 200 = 8000000
When we multiply the cube root of 1000000 by 2, it results in an increase in volume because the cube of the new value, 200, is 8000000.
Find ∛(500000+500000).
∛(500000+500000) = ∛1000000 = 100
As shown in the question ∛(500000+500000), we can simplify that by adding them. So, 500000 + 500000 = 1000000. Then we use this step: ∛1000000 = 100 to get the answer.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.